MAYBE

Initial complexity problem:
1:	T:
		(?, 1)    f2(a, b) -> f2(a - 1, b) [ a >= 1 ]
		(1, 1)    f0(a, b) -> f2(c, b - 1) [ b >= 1 ]
		(?, 1)    f2(a, b) -> f2(c, b - 1) [ b >= 1 /\ 0 >= a ]
	start location:	f0
	leaf cost:	0

A polynomial rank function with
	Pol(f2) = V_2
	Pol(f0) = V_2
orients all transitions weakly and the transition
	f2(a, b) -> f2(c, b - 1) [ b >= 1 /\ 0 >= a ]
strictly and produces the following problem:
2:	T:
		(?, 1)    f2(a, b) -> f2(a - 1, b) [ a >= 1 ]
		(1, 1)    f0(a, b) -> f2(c, b - 1) [ b >= 1 ]
		(b, 1)    f2(a, b) -> f2(c, b - 1) [ b >= 1 /\ 0 >= a ]
	start location:	f0
	leaf cost:	0

Applied AI with 'oct' on problem 2 to obtain the following invariants:
  For symbol f2: X_2 >= 0


This yielded the following problem:
3:	T:
		(b, 1)    f2(a, b) -> f2(c, b - 1) [ b >= 0 /\ b >= 1 /\ 0 >= a ]
		(1, 1)    f0(a, b) -> f2(c, b - 1) [ b >= 1 ]
		(?, 1)    f2(a, b) -> f2(a - 1, b) [ b >= 0 /\ a >= 1 ]
	start location:	f0
	leaf cost:	0

By chaining the transition f0(a, b) -> f2(c, b - 1) [ b >= 1 ] with all transitions in problem 3, the following new transitions are obtained:
	f0(a, b) -> f2(c - 1, b - 1) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 ]
	f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ b - 1 >= 1 /\ 0 >= c ]
We thus obtain the following problem:
4:	T:
		(1, 2)    f0(a, b) -> f2(c - 1, b - 1) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 ]
		(1, 2)    f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ b - 1 >= 1 /\ 0 >= c ]
		(b, 1)    f2(a, b) -> f2(c, b - 1) [ b >= 0 /\ b >= 1 /\ 0 >= a ]
		(?, 1)    f2(a, b) -> f2(a - 1, b) [ b >= 0 /\ a >= 1 ]
	start location:	f0
	leaf cost:	0

By chaining the transition f0(a, b) -> f2(c - 1, b - 1) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 ] with all transitions in problem 4, the following new transitions are obtained:
	f0(a, b) -> f2(c - 2, b - 1) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 ]
	f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ b - 1 >= 1 /\ 0 >= c - 1 ]
We thus obtain the following problem:
5:	T:
		(1, 3)    f0(a, b) -> f2(c - 2, b - 1) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 ]
		(1, 3)    f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ b - 1 >= 1 /\ 0 >= c - 1 ]
		(1, 2)    f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ b - 1 >= 1 /\ 0 >= c ]
		(b, 1)    f2(a, b) -> f2(c, b - 1) [ b >= 0 /\ b >= 1 /\ 0 >= a ]
		(?, 1)    f2(a, b) -> f2(a - 1, b) [ b >= 0 /\ a >= 1 ]
	start location:	f0
	leaf cost:	0

By chaining the transition f0(a, b) -> f2(c - 2, b - 1) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 ] with all transitions in problem 5, the following new transitions are obtained:
	f0(a, b) -> f2(c - 3, b - 1) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 ]
	f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ b - 1 >= 1 /\ 0 >= c - 2 ]
We thus obtain the following problem:
6:	T:
		(1, 4)    f0(a, b) -> f2(c - 3, b - 1) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 ]
		(1, 4)    f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ b - 1 >= 1 /\ 0 >= c - 2 ]
		(1, 3)    f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ b - 1 >= 1 /\ 0 >= c - 1 ]
		(1, 2)    f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ b - 1 >= 1 /\ 0 >= c ]
		(b, 1)    f2(a, b) -> f2(c, b - 1) [ b >= 0 /\ b >= 1 /\ 0 >= a ]
		(?, 1)    f2(a, b) -> f2(a - 1, b) [ b >= 0 /\ a >= 1 ]
	start location:	f0
	leaf cost:	0

By chaining the transition f0(a, b) -> f2(c - 3, b - 1) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 ] with all transitions in problem 6, the following new transitions are obtained:
	f0(a, b) -> f2(c - 4, b - 1) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 ]
	f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ b - 1 >= 1 /\ 0 >= c - 3 ]
We thus obtain the following problem:
7:	T:
		(1, 5)    f0(a, b) -> f2(c - 4, b - 1) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 ]
		(1, 5)    f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ b - 1 >= 1 /\ 0 >= c - 3 ]
		(1, 4)    f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ b - 1 >= 1 /\ 0 >= c - 2 ]
		(1, 3)    f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ b - 1 >= 1 /\ 0 >= c - 1 ]
		(1, 2)    f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ b - 1 >= 1 /\ 0 >= c ]
		(b, 1)    f2(a, b) -> f2(c, b - 1) [ b >= 0 /\ b >= 1 /\ 0 >= a ]
		(?, 1)    f2(a, b) -> f2(a - 1, b) [ b >= 0 /\ a >= 1 ]
	start location:	f0
	leaf cost:	0

By chaining the transition f0(a, b) -> f2(c - 4, b - 1) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 ] with all transitions in problem 7, the following new transitions are obtained:
	f0(a, b) -> f2(c - 5, b - 1) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ c - 4 >= 1 ]
	f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ b - 1 >= 1 /\ 0 >= c - 4 ]
We thus obtain the following problem:
8:	T:
		(1, 6)    f0(a, b) -> f2(c - 5, b - 1) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ c - 4 >= 1 ]
		(1, 6)    f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ b - 1 >= 1 /\ 0 >= c - 4 ]
		(1, 5)    f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ b - 1 >= 1 /\ 0 >= c - 3 ]
		(1, 4)    f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ b - 1 >= 1 /\ 0 >= c - 2 ]
		(1, 3)    f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ b - 1 >= 1 /\ 0 >= c - 1 ]
		(1, 2)    f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ b - 1 >= 1 /\ 0 >= c ]
		(b, 1)    f2(a, b) -> f2(c, b - 1) [ b >= 0 /\ b >= 1 /\ 0 >= a ]
		(?, 1)    f2(a, b) -> f2(a - 1, b) [ b >= 0 /\ a >= 1 ]
	start location:	f0
	leaf cost:	0

By chaining the transition f0(a, b) -> f2(c - 5, b - 1) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ c - 4 >= 1 ] with all transitions in problem 8, the following new transitions are obtained:
	f0(a, b) -> f2(c - 6, b - 1) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ c - 4 >= 1 /\ c - 5 >= 1 ]
	f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ c - 4 >= 1 /\ b - 1 >= 1 /\ 0 >= c - 5 ]
We thus obtain the following problem:
9:	T:
		(1, 7)    f0(a, b) -> f2(c - 6, b - 1) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ c - 4 >= 1 /\ c - 5 >= 1 ]
		(1, 7)    f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ c - 4 >= 1 /\ b - 1 >= 1 /\ 0 >= c - 5 ]
		(1, 6)    f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ b - 1 >= 1 /\ 0 >= c - 4 ]
		(1, 5)    f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ b - 1 >= 1 /\ 0 >= c - 3 ]
		(1, 4)    f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ b - 1 >= 1 /\ 0 >= c - 2 ]
		(1, 3)    f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ b - 1 >= 1 /\ 0 >= c - 1 ]
		(1, 2)    f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ b - 1 >= 1 /\ 0 >= c ]
		(b, 1)    f2(a, b) -> f2(c, b - 1) [ b >= 0 /\ b >= 1 /\ 0 >= a ]
		(?, 1)    f2(a, b) -> f2(a - 1, b) [ b >= 0 /\ a >= 1 ]
	start location:	f0
	leaf cost:	0

By chaining the transition f0(a, b) -> f2(c - 6, b - 1) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ c - 4 >= 1 /\ c - 5 >= 1 ] with all transitions in problem 9, the following new transitions are obtained:
	f0(a, b) -> f2(c - 7, b - 1) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ c - 4 >= 1 /\ c - 5 >= 1 /\ c - 6 >= 1 ]
	f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ c - 4 >= 1 /\ c - 5 >= 1 /\ b - 1 >= 1 /\ 0 >= c - 6 ]
We thus obtain the following problem:
10:	T:
		(1, 8)    f0(a, b) -> f2(c - 7, b - 1) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ c - 4 >= 1 /\ c - 5 >= 1 /\ c - 6 >= 1 ]
		(1, 8)    f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ c - 4 >= 1 /\ c - 5 >= 1 /\ b - 1 >= 1 /\ 0 >= c - 6 ]
		(1, 7)    f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ c - 4 >= 1 /\ b - 1 >= 1 /\ 0 >= c - 5 ]
		(1, 6)    f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ b - 1 >= 1 /\ 0 >= c - 4 ]
		(1, 5)    f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ b - 1 >= 1 /\ 0 >= c - 3 ]
		(1, 4)    f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ b - 1 >= 1 /\ 0 >= c - 2 ]
		(1, 3)    f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ b - 1 >= 1 /\ 0 >= c - 1 ]
		(1, 2)    f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ b - 1 >= 1 /\ 0 >= c ]
		(b, 1)    f2(a, b) -> f2(c, b - 1) [ b >= 0 /\ b >= 1 /\ 0 >= a ]
		(?, 1)    f2(a, b) -> f2(a - 1, b) [ b >= 0 /\ a >= 1 ]
	start location:	f0
	leaf cost:	0

By chaining the transition f0(a, b) -> f2(c - 7, b - 1) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ c - 4 >= 1 /\ c - 5 >= 1 /\ c - 6 >= 1 ] with all transitions in problem 10, the following new transitions are obtained:
	f0(a, b) -> f2(c - 8, b - 1) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ c - 4 >= 1 /\ c - 5 >= 1 /\ c - 6 >= 1 /\ c - 7 >= 1 ]
	f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ c - 4 >= 1 /\ c - 5 >= 1 /\ c - 6 >= 1 /\ b - 1 >= 1 /\ 0 >= c - 7 ]
We thus obtain the following problem:
11:	T:
		(1, 9)    f0(a, b) -> f2(c - 8, b - 1) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ c - 4 >= 1 /\ c - 5 >= 1 /\ c - 6 >= 1 /\ c - 7 >= 1 ]
		(1, 9)    f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ c - 4 >= 1 /\ c - 5 >= 1 /\ c - 6 >= 1 /\ b - 1 >= 1 /\ 0 >= c - 7 ]
		(1, 8)    f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ c - 4 >= 1 /\ c - 5 >= 1 /\ b - 1 >= 1 /\ 0 >= c - 6 ]
		(1, 7)    f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ c - 4 >= 1 /\ b - 1 >= 1 /\ 0 >= c - 5 ]
		(1, 6)    f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ b - 1 >= 1 /\ 0 >= c - 4 ]
		(1, 5)    f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ b - 1 >= 1 /\ 0 >= c - 3 ]
		(1, 4)    f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ b - 1 >= 1 /\ 0 >= c - 2 ]
		(1, 3)    f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ b - 1 >= 1 /\ 0 >= c - 1 ]
		(1, 2)    f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ b - 1 >= 1 /\ 0 >= c ]
		(b, 1)    f2(a, b) -> f2(c, b - 1) [ b >= 0 /\ b >= 1 /\ 0 >= a ]
		(?, 1)    f2(a, b) -> f2(a - 1, b) [ b >= 0 /\ a >= 1 ]
	start location:	f0
	leaf cost:	0

By chaining the transition f0(a, b) -> f2(c - 8, b - 1) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ c - 4 >= 1 /\ c - 5 >= 1 /\ c - 6 >= 1 /\ c - 7 >= 1 ] with all transitions in problem 11, the following new transitions are obtained:
	f0(a, b) -> f2(c - 9, b - 1) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ c - 4 >= 1 /\ c - 5 >= 1 /\ c - 6 >= 1 /\ c - 7 >= 1 /\ c - 8 >= 1 ]
	f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ c - 4 >= 1 /\ c - 5 >= 1 /\ c - 6 >= 1 /\ c - 7 >= 1 /\ b - 1 >= 1 /\ 0 >= c - 8 ]
We thus obtain the following problem:
12:	T:
		(1, 10)    f0(a, b) -> f2(c - 9, b - 1) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ c - 4 >= 1 /\ c - 5 >= 1 /\ c - 6 >= 1 /\ c - 7 >= 1 /\ c - 8 >= 1 ]
		(1, 10)    f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ c - 4 >= 1 /\ c - 5 >= 1 /\ c - 6 >= 1 /\ c - 7 >= 1 /\ b - 1 >= 1 /\ 0 >= c - 8 ]
		(1, 9)     f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ c - 4 >= 1 /\ c - 5 >= 1 /\ c - 6 >= 1 /\ b - 1 >= 1 /\ 0 >= c - 7 ]
		(1, 8)     f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ c - 4 >= 1 /\ c - 5 >= 1 /\ b - 1 >= 1 /\ 0 >= c - 6 ]
		(1, 7)     f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ c - 4 >= 1 /\ b - 1 >= 1 /\ 0 >= c - 5 ]
		(1, 6)     f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ b - 1 >= 1 /\ 0 >= c - 4 ]
		(1, 5)     f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ b - 1 >= 1 /\ 0 >= c - 3 ]
		(1, 4)     f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ b - 1 >= 1 /\ 0 >= c - 2 ]
		(1, 3)     f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ b - 1 >= 1 /\ 0 >= c - 1 ]
		(1, 2)     f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ b - 1 >= 1 /\ 0 >= c ]
		(b, 1)     f2(a, b) -> f2(c, b - 1) [ b >= 0 /\ b >= 1 /\ 0 >= a ]
		(?, 1)     f2(a, b) -> f2(a - 1, b) [ b >= 0 /\ a >= 1 ]
	start location:	f0
	leaf cost:	0

By chaining the transition f0(a, b) -> f2(c - 9, b - 1) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ c - 4 >= 1 /\ c - 5 >= 1 /\ c - 6 >= 1 /\ c - 7 >= 1 /\ c - 8 >= 1 ] with all transitions in problem 12, the following new transitions are obtained:
	f0(a, b) -> f2(c - 10, b - 1) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ c - 4 >= 1 /\ c - 5 >= 1 /\ c - 6 >= 1 /\ c - 7 >= 1 /\ c - 8 >= 1 /\ c - 9 >= 1 ]
	f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ c - 4 >= 1 /\ c - 5 >= 1 /\ c - 6 >= 1 /\ c - 7 >= 1 /\ c - 8 >= 1 /\ b - 1 >= 1 /\ 0 >= c - 9 ]
We thus obtain the following problem:
13:	T:
		(1, 11)    f0(a, b) -> f2(c - 10, b - 1) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ c - 4 >= 1 /\ c - 5 >= 1 /\ c - 6 >= 1 /\ c - 7 >= 1 /\ c - 8 >= 1 /\ c - 9 >= 1 ]
		(1, 11)    f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ c - 4 >= 1 /\ c - 5 >= 1 /\ c - 6 >= 1 /\ c - 7 >= 1 /\ c - 8 >= 1 /\ b - 1 >= 1 /\ 0 >= c - 9 ]
		(1, 10)    f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ c - 4 >= 1 /\ c - 5 >= 1 /\ c - 6 >= 1 /\ c - 7 >= 1 /\ b - 1 >= 1 /\ 0 >= c - 8 ]
		(1, 9)     f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ c - 4 >= 1 /\ c - 5 >= 1 /\ c - 6 >= 1 /\ b - 1 >= 1 /\ 0 >= c - 7 ]
		(1, 8)     f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ c - 4 >= 1 /\ c - 5 >= 1 /\ b - 1 >= 1 /\ 0 >= c - 6 ]
		(1, 7)     f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ c - 4 >= 1 /\ b - 1 >= 1 /\ 0 >= c - 5 ]
		(1, 6)     f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ b - 1 >= 1 /\ 0 >= c - 4 ]
		(1, 5)     f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ b - 1 >= 1 /\ 0 >= c - 3 ]
		(1, 4)     f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ b - 1 >= 1 /\ 0 >= c - 2 ]
		(1, 3)     f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ b - 1 >= 1 /\ 0 >= c - 1 ]
		(1, 2)     f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ b - 1 >= 1 /\ 0 >= c ]
		(b, 1)     f2(a, b) -> f2(c, b - 1) [ b >= 0 /\ b >= 1 /\ 0 >= a ]
		(?, 1)     f2(a, b) -> f2(a - 1, b) [ b >= 0 /\ a >= 1 ]
	start location:	f0
	leaf cost:	0

By chaining the transition f0(a, b) -> f2(c - 10, b - 1) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ c - 4 >= 1 /\ c - 5 >= 1 /\ c - 6 >= 1 /\ c - 7 >= 1 /\ c - 8 >= 1 /\ c - 9 >= 1 ] with all transitions in problem 13, the following new transitions are obtained:
	f0(a, b) -> f2(c - 11, b - 1) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ c - 4 >= 1 /\ c - 5 >= 1 /\ c - 6 >= 1 /\ c - 7 >= 1 /\ c - 8 >= 1 /\ c - 9 >= 1 /\ c - 10 >= 1 ]
	f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ c - 4 >= 1 /\ c - 5 >= 1 /\ c - 6 >= 1 /\ c - 7 >= 1 /\ c - 8 >= 1 /\ c - 9 >= 1 /\ b - 1 >= 1 /\ 0 >= c - 10 ]
We thus obtain the following problem:
14:	T:
		(1, 12)    f0(a, b) -> f2(c - 11, b - 1) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ c - 4 >= 1 /\ c - 5 >= 1 /\ c - 6 >= 1 /\ c - 7 >= 1 /\ c - 8 >= 1 /\ c - 9 >= 1 /\ c - 10 >= 1 ]
		(1, 12)    f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ c - 4 >= 1 /\ c - 5 >= 1 /\ c - 6 >= 1 /\ c - 7 >= 1 /\ c - 8 >= 1 /\ c - 9 >= 1 /\ b - 1 >= 1 /\ 0 >= c - 10 ]
		(1, 11)    f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ c - 4 >= 1 /\ c - 5 >= 1 /\ c - 6 >= 1 /\ c - 7 >= 1 /\ c - 8 >= 1 /\ b - 1 >= 1 /\ 0 >= c - 9 ]
		(1, 10)    f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ c - 4 >= 1 /\ c - 5 >= 1 /\ c - 6 >= 1 /\ c - 7 >= 1 /\ b - 1 >= 1 /\ 0 >= c - 8 ]
		(1, 9)     f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ c - 4 >= 1 /\ c - 5 >= 1 /\ c - 6 >= 1 /\ b - 1 >= 1 /\ 0 >= c - 7 ]
		(1, 8)     f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ c - 4 >= 1 /\ c - 5 >= 1 /\ b - 1 >= 1 /\ 0 >= c - 6 ]
		(1, 7)     f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ c - 4 >= 1 /\ b - 1 >= 1 /\ 0 >= c - 5 ]
		(1, 6)     f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ b - 1 >= 1 /\ 0 >= c - 4 ]
		(1, 5)     f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ b - 1 >= 1 /\ 0 >= c - 3 ]
		(1, 4)     f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ b - 1 >= 1 /\ 0 >= c - 2 ]
		(1, 3)     f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ b - 1 >= 1 /\ 0 >= c - 1 ]
		(1, 2)     f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ b - 1 >= 1 /\ 0 >= c ]
		(b, 1)     f2(a, b) -> f2(c, b - 1) [ b >= 0 /\ b >= 1 /\ 0 >= a ]
		(?, 1)     f2(a, b) -> f2(a - 1, b) [ b >= 0 /\ a >= 1 ]
	start location:	f0
	leaf cost:	0

By chaining the transition f0(a, b) -> f2(c - 11, b - 1) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ c - 4 >= 1 /\ c - 5 >= 1 /\ c - 6 >= 1 /\ c - 7 >= 1 /\ c - 8 >= 1 /\ c - 9 >= 1 /\ c - 10 >= 1 ] with all transitions in problem 14, the following new transitions are obtained:
	f0(a, b) -> f2(c - 12, b - 1) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ c - 4 >= 1 /\ c - 5 >= 1 /\ c - 6 >= 1 /\ c - 7 >= 1 /\ c - 8 >= 1 /\ c - 9 >= 1 /\ c - 10 >= 1 /\ c - 11 >= 1 ]
	f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ c - 4 >= 1 /\ c - 5 >= 1 /\ c - 6 >= 1 /\ c - 7 >= 1 /\ c - 8 >= 1 /\ c - 9 >= 1 /\ c - 10 >= 1 /\ b - 1 >= 1 /\ 0 >= c - 11 ]
We thus obtain the following problem:
15:	T:
		(1, 13)    f0(a, b) -> f2(c - 12, b - 1) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ c - 4 >= 1 /\ c - 5 >= 1 /\ c - 6 >= 1 /\ c - 7 >= 1 /\ c - 8 >= 1 /\ c - 9 >= 1 /\ c - 10 >= 1 /\ c - 11 >= 1 ]
		(1, 13)    f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ c - 4 >= 1 /\ c - 5 >= 1 /\ c - 6 >= 1 /\ c - 7 >= 1 /\ c - 8 >= 1 /\ c - 9 >= 1 /\ c - 10 >= 1 /\ b - 1 >= 1 /\ 0 >= c - 11 ]
		(1, 12)    f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ c - 4 >= 1 /\ c - 5 >= 1 /\ c - 6 >= 1 /\ c - 7 >= 1 /\ c - 8 >= 1 /\ c - 9 >= 1 /\ b - 1 >= 1 /\ 0 >= c - 10 ]
		(1, 11)    f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ c - 4 >= 1 /\ c - 5 >= 1 /\ c - 6 >= 1 /\ c - 7 >= 1 /\ c - 8 >= 1 /\ b - 1 >= 1 /\ 0 >= c - 9 ]
		(1, 10)    f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ c - 4 >= 1 /\ c - 5 >= 1 /\ c - 6 >= 1 /\ c - 7 >= 1 /\ b - 1 >= 1 /\ 0 >= c - 8 ]
		(1, 9)     f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ c - 4 >= 1 /\ c - 5 >= 1 /\ c - 6 >= 1 /\ b - 1 >= 1 /\ 0 >= c - 7 ]
		(1, 8)     f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ c - 4 >= 1 /\ c - 5 >= 1 /\ b - 1 >= 1 /\ 0 >= c - 6 ]
		(1, 7)     f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ c - 4 >= 1 /\ b - 1 >= 1 /\ 0 >= c - 5 ]
		(1, 6)     f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ b - 1 >= 1 /\ 0 >= c - 4 ]
		(1, 5)     f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ b - 1 >= 1 /\ 0 >= c - 3 ]
		(1, 4)     f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ b - 1 >= 1 /\ 0 >= c - 2 ]
		(1, 3)     f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ b - 1 >= 1 /\ 0 >= c - 1 ]
		(1, 2)     f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ b - 1 >= 1 /\ 0 >= c ]
		(b, 1)     f2(a, b) -> f2(c, b - 1) [ b >= 0 /\ b >= 1 /\ 0 >= a ]
		(?, 1)     f2(a, b) -> f2(a - 1, b) [ b >= 0 /\ a >= 1 ]
	start location:	f0
	leaf cost:	0

By chaining the transition f0(a, b) -> f2(c - 12, b - 1) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ c - 4 >= 1 /\ c - 5 >= 1 /\ c - 6 >= 1 /\ c - 7 >= 1 /\ c - 8 >= 1 /\ c - 9 >= 1 /\ c - 10 >= 1 /\ c - 11 >= 1 ] with all transitions in problem 15, the following new transitions are obtained:
	f0(a, b) -> f2(c - 13, b - 1) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ c - 4 >= 1 /\ c - 5 >= 1 /\ c - 6 >= 1 /\ c - 7 >= 1 /\ c - 8 >= 1 /\ c - 9 >= 1 /\ c - 10 >= 1 /\ c - 11 >= 1 /\ c - 12 >= 1 ]
	f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ c - 4 >= 1 /\ c - 5 >= 1 /\ c - 6 >= 1 /\ c - 7 >= 1 /\ c - 8 >= 1 /\ c - 9 >= 1 /\ c - 10 >= 1 /\ c - 11 >= 1 /\ b - 1 >= 1 /\ 0 >= c - 12 ]
We thus obtain the following problem:
16:	T:
		(1, 14)    f0(a, b) -> f2(c - 13, b - 1) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ c - 4 >= 1 /\ c - 5 >= 1 /\ c - 6 >= 1 /\ c - 7 >= 1 /\ c - 8 >= 1 /\ c - 9 >= 1 /\ c - 10 >= 1 /\ c - 11 >= 1 /\ c - 12 >= 1 ]
		(1, 14)    f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ c - 4 >= 1 /\ c - 5 >= 1 /\ c - 6 >= 1 /\ c - 7 >= 1 /\ c - 8 >= 1 /\ c - 9 >= 1 /\ c - 10 >= 1 /\ c - 11 >= 1 /\ b - 1 >= 1 /\ 0 >= c - 12 ]
		(1, 13)    f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ c - 4 >= 1 /\ c - 5 >= 1 /\ c - 6 >= 1 /\ c - 7 >= 1 /\ c - 8 >= 1 /\ c - 9 >= 1 /\ c - 10 >= 1 /\ b - 1 >= 1 /\ 0 >= c - 11 ]
		(1, 12)    f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ c - 4 >= 1 /\ c - 5 >= 1 /\ c - 6 >= 1 /\ c - 7 >= 1 /\ c - 8 >= 1 /\ c - 9 >= 1 /\ b - 1 >= 1 /\ 0 >= c - 10 ]
		(1, 11)    f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ c - 4 >= 1 /\ c - 5 >= 1 /\ c - 6 >= 1 /\ c - 7 >= 1 /\ c - 8 >= 1 /\ b - 1 >= 1 /\ 0 >= c - 9 ]
		(1, 10)    f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ c - 4 >= 1 /\ c - 5 >= 1 /\ c - 6 >= 1 /\ c - 7 >= 1 /\ b - 1 >= 1 /\ 0 >= c - 8 ]
		(1, 9)     f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ c - 4 >= 1 /\ c - 5 >= 1 /\ c - 6 >= 1 /\ b - 1 >= 1 /\ 0 >= c - 7 ]
		(1, 8)     f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ c - 4 >= 1 /\ c - 5 >= 1 /\ b - 1 >= 1 /\ 0 >= c - 6 ]
		(1, 7)     f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ c - 4 >= 1 /\ b - 1 >= 1 /\ 0 >= c - 5 ]
		(1, 6)     f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ b - 1 >= 1 /\ 0 >= c - 4 ]
		(1, 5)     f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ b - 1 >= 1 /\ 0 >= c - 3 ]
		(1, 4)     f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ b - 1 >= 1 /\ 0 >= c - 2 ]
		(1, 3)     f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ b - 1 >= 1 /\ 0 >= c - 1 ]
		(1, 2)     f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ b - 1 >= 1 /\ 0 >= c ]
		(b, 1)     f2(a, b) -> f2(c, b - 1) [ b >= 0 /\ b >= 1 /\ 0 >= a ]
		(?, 1)     f2(a, b) -> f2(a - 1, b) [ b >= 0 /\ a >= 1 ]
	start location:	f0
	leaf cost:	0

By chaining the transition f0(a, b) -> f2(c - 13, b - 1) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ c - 4 >= 1 /\ c - 5 >= 1 /\ c - 6 >= 1 /\ c - 7 >= 1 /\ c - 8 >= 1 /\ c - 9 >= 1 /\ c - 10 >= 1 /\ c - 11 >= 1 /\ c - 12 >= 1 ] with all transitions in problem 16, the following new transitions are obtained:
	f0(a, b) -> f2(c - 14, b - 1) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ c - 4 >= 1 /\ c - 5 >= 1 /\ c - 6 >= 1 /\ c - 7 >= 1 /\ c - 8 >= 1 /\ c - 9 >= 1 /\ c - 10 >= 1 /\ c - 11 >= 1 /\ c - 12 >= 1 /\ c - 13 >= 1 ]
	f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ c - 4 >= 1 /\ c - 5 >= 1 /\ c - 6 >= 1 /\ c - 7 >= 1 /\ c - 8 >= 1 /\ c - 9 >= 1 /\ c - 10 >= 1 /\ c - 11 >= 1 /\ c - 12 >= 1 /\ b - 1 >= 1 /\ 0 >= c - 13 ]
We thus obtain the following problem:
17:	T:
		(1, 15)    f0(a, b) -> f2(c - 14, b - 1) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ c - 4 >= 1 /\ c - 5 >= 1 /\ c - 6 >= 1 /\ c - 7 >= 1 /\ c - 8 >= 1 /\ c - 9 >= 1 /\ c - 10 >= 1 /\ c - 11 >= 1 /\ c - 12 >= 1 /\ c - 13 >= 1 ]
		(1, 15)    f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ c - 4 >= 1 /\ c - 5 >= 1 /\ c - 6 >= 1 /\ c - 7 >= 1 /\ c - 8 >= 1 /\ c - 9 >= 1 /\ c - 10 >= 1 /\ c - 11 >= 1 /\ c - 12 >= 1 /\ b - 1 >= 1 /\ 0 >= c - 13 ]
		(1, 14)    f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ c - 4 >= 1 /\ c - 5 >= 1 /\ c - 6 >= 1 /\ c - 7 >= 1 /\ c - 8 >= 1 /\ c - 9 >= 1 /\ c - 10 >= 1 /\ c - 11 >= 1 /\ b - 1 >= 1 /\ 0 >= c - 12 ]
		(1, 13)    f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ c - 4 >= 1 /\ c - 5 >= 1 /\ c - 6 >= 1 /\ c - 7 >= 1 /\ c - 8 >= 1 /\ c - 9 >= 1 /\ c - 10 >= 1 /\ b - 1 >= 1 /\ 0 >= c - 11 ]
		(1, 12)    f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ c - 4 >= 1 /\ c - 5 >= 1 /\ c - 6 >= 1 /\ c - 7 >= 1 /\ c - 8 >= 1 /\ c - 9 >= 1 /\ b - 1 >= 1 /\ 0 >= c - 10 ]
		(1, 11)    f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ c - 4 >= 1 /\ c - 5 >= 1 /\ c - 6 >= 1 /\ c - 7 >= 1 /\ c - 8 >= 1 /\ b - 1 >= 1 /\ 0 >= c - 9 ]
		(1, 10)    f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ c - 4 >= 1 /\ c - 5 >= 1 /\ c - 6 >= 1 /\ c - 7 >= 1 /\ b - 1 >= 1 /\ 0 >= c - 8 ]
		(1, 9)     f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ c - 4 >= 1 /\ c - 5 >= 1 /\ c - 6 >= 1 /\ b - 1 >= 1 /\ 0 >= c - 7 ]
		(1, 8)     f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ c - 4 >= 1 /\ c - 5 >= 1 /\ b - 1 >= 1 /\ 0 >= c - 6 ]
		(1, 7)     f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ c - 4 >= 1 /\ b - 1 >= 1 /\ 0 >= c - 5 ]
		(1, 6)     f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ b - 1 >= 1 /\ 0 >= c - 4 ]
		(1, 5)     f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ b - 1 >= 1 /\ 0 >= c - 3 ]
		(1, 4)     f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ b - 1 >= 1 /\ 0 >= c - 2 ]
		(1, 3)     f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ b - 1 >= 1 /\ 0 >= c - 1 ]
		(1, 2)     f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ b - 1 >= 1 /\ 0 >= c ]
		(b, 1)     f2(a, b) -> f2(c, b - 1) [ b >= 0 /\ b >= 1 /\ 0 >= a ]
		(?, 1)     f2(a, b) -> f2(a - 1, b) [ b >= 0 /\ a >= 1 ]
	start location:	f0
	leaf cost:	0

By chaining the transition f0(a, b) -> f2(c - 14, b - 1) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ c - 4 >= 1 /\ c - 5 >= 1 /\ c - 6 >= 1 /\ c - 7 >= 1 /\ c - 8 >= 1 /\ c - 9 >= 1 /\ c - 10 >= 1 /\ c - 11 >= 1 /\ c - 12 >= 1 /\ c - 13 >= 1 ] with all transitions in problem 17, the following new transitions are obtained:
	f0(a, b) -> f2(c - 15, b - 1) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ c - 4 >= 1 /\ c - 5 >= 1 /\ c - 6 >= 1 /\ c - 7 >= 1 /\ c - 8 >= 1 /\ c - 9 >= 1 /\ c - 10 >= 1 /\ c - 11 >= 1 /\ c - 12 >= 1 /\ c - 13 >= 1 /\ c - 14 >= 1 ]
	f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ c - 4 >= 1 /\ c - 5 >= 1 /\ c - 6 >= 1 /\ c - 7 >= 1 /\ c - 8 >= 1 /\ c - 9 >= 1 /\ c - 10 >= 1 /\ c - 11 >= 1 /\ c - 12 >= 1 /\ c - 13 >= 1 /\ b - 1 >= 1 /\ 0 >= c - 14 ]
We thus obtain the following problem:
18:	T:
		(1, 16)    f0(a, b) -> f2(c - 15, b - 1) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ c - 4 >= 1 /\ c - 5 >= 1 /\ c - 6 >= 1 /\ c - 7 >= 1 /\ c - 8 >= 1 /\ c - 9 >= 1 /\ c - 10 >= 1 /\ c - 11 >= 1 /\ c - 12 >= 1 /\ c - 13 >= 1 /\ c - 14 >= 1 ]
		(1, 16)    f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ c - 4 >= 1 /\ c - 5 >= 1 /\ c - 6 >= 1 /\ c - 7 >= 1 /\ c - 8 >= 1 /\ c - 9 >= 1 /\ c - 10 >= 1 /\ c - 11 >= 1 /\ c - 12 >= 1 /\ c - 13 >= 1 /\ b - 1 >= 1 /\ 0 >= c - 14 ]
		(1, 15)    f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ c - 4 >= 1 /\ c - 5 >= 1 /\ c - 6 >= 1 /\ c - 7 >= 1 /\ c - 8 >= 1 /\ c - 9 >= 1 /\ c - 10 >= 1 /\ c - 11 >= 1 /\ c - 12 >= 1 /\ b - 1 >= 1 /\ 0 >= c - 13 ]
		(1, 14)    f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ c - 4 >= 1 /\ c - 5 >= 1 /\ c - 6 >= 1 /\ c - 7 >= 1 /\ c - 8 >= 1 /\ c - 9 >= 1 /\ c - 10 >= 1 /\ c - 11 >= 1 /\ b - 1 >= 1 /\ 0 >= c - 12 ]
		(1, 13)    f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ c - 4 >= 1 /\ c - 5 >= 1 /\ c - 6 >= 1 /\ c - 7 >= 1 /\ c - 8 >= 1 /\ c - 9 >= 1 /\ c - 10 >= 1 /\ b - 1 >= 1 /\ 0 >= c - 11 ]
		(1, 12)    f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ c - 4 >= 1 /\ c - 5 >= 1 /\ c - 6 >= 1 /\ c - 7 >= 1 /\ c - 8 >= 1 /\ c - 9 >= 1 /\ b - 1 >= 1 /\ 0 >= c - 10 ]
		(1, 11)    f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ c - 4 >= 1 /\ c - 5 >= 1 /\ c - 6 >= 1 /\ c - 7 >= 1 /\ c - 8 >= 1 /\ b - 1 >= 1 /\ 0 >= c - 9 ]
		(1, 10)    f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ c - 4 >= 1 /\ c - 5 >= 1 /\ c - 6 >= 1 /\ c - 7 >= 1 /\ b - 1 >= 1 /\ 0 >= c - 8 ]
		(1, 9)     f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ c - 4 >= 1 /\ c - 5 >= 1 /\ c - 6 >= 1 /\ b - 1 >= 1 /\ 0 >= c - 7 ]
		(1, 8)     f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ c - 4 >= 1 /\ c - 5 >= 1 /\ b - 1 >= 1 /\ 0 >= c - 6 ]
		(1, 7)     f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ c - 4 >= 1 /\ b - 1 >= 1 /\ 0 >= c - 5 ]
		(1, 6)     f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ c - 3 >= 1 /\ b - 1 >= 1 /\ 0 >= c - 4 ]
		(1, 5)     f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ c - 2 >= 1 /\ b - 1 >= 1 /\ 0 >= c - 3 ]
		(1, 4)     f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ c - 1 >= 1 /\ b - 1 >= 1 /\ 0 >= c - 2 ]
		(1, 3)     f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ c >= 1 /\ b - 1 >= 1 /\ 0 >= c - 1 ]
		(1, 2)     f0(a, b) -> f2(c', b - 2) [ b >= 1 /\ b - 1 >= 0 /\ b - 1 >= 1 /\ 0 >= c ]
		(b, 1)     f2(a, b) -> f2(c, b - 1) [ b >= 0 /\ b >= 1 /\ 0 >= a ]
		(?, 1)     f2(a, b) -> f2(a - 1, b) [ b >= 0 /\ a >= 1 ]
	start location:	f0
	leaf cost:	0

Complexity upper bound ?

Time: 2.592 sec (SMT: 2.416 sec)